![matrices - Prove that the determinant is $(a-b)(b-c)(c-a)(a^2 + b^2 + c^2 )$ - Mathematics Stack Exchange matrices - Prove that the determinant is $(a-b)(b-c)(c-a)(a^2 + b^2 + c^2 )$ - Mathematics Stack Exchange](https://i.stack.imgur.com/WqPIX.jpg)
matrices - Prove that the determinant is $(a-b)(b-c)(c-a)(a^2 + b^2 + c^2 )$ - Mathematics Stack Exchange
![i) If a^(2)+b^(2)+c^(2)=20 " and" a+b+c=0, " find " ab+bc+ac. (ii) If a^(2)+ b^(2)+c^(2)=250 " and" ab+bc+ca=3, " find" a+b+c. (iii) If a+b+c=11 and ab+ bc+ca=25, then find the value of a^(3)+b^(3)+c^(3)-3 abc. i) If a^(2)+b^(2)+c^(2)=20 " and" a+b+c=0, " find " ab+bc+ac. (ii) If a^(2)+ b^(2)+c^(2)=250 " and" ab+bc+ca=3, " find" a+b+c. (iii) If a+b+c=11 and ab+ bc+ca=25, then find the value of a^(3)+b^(3)+c^(3)-3 abc.](https://d10lpgp6xz60nq.cloudfront.net/ss/web/669619.jpg)
i) If a^(2)+b^(2)+c^(2)=20 " and" a+b+c=0, " find " ab+bc+ac. (ii) If a^(2)+ b^(2)+c^(2)=250 " and" ab+bc+ca=3, " find" a+b+c. (iii) If a+b+c=11 and ab+ bc+ca=25, then find the value of a^(3)+b^(3)+c^(3)-3 abc.
![if a+b+c=8, a2+b2+c2=30,find the value of ab+bc+ca - Maths - Polynomials - 4662937 | Meritnation.com if a+b+c=8, a2+b2+c2=30,find the value of ab+bc+ca - Maths - Polynomials - 4662937 | Meritnation.com](https://s3mn.mnimgs.com/img/shared/discuss_editlive/3781436/2013_04_29_12_46_05/mathmlequation7523069594225382366.png)